In an XY coordinate plane, the line x = 5 is a perpendicular bisector

Question

In an XY coordinate plane, the line x = 5 is a perpendicular bisector of the line segment AB. If the coordinates of point A are (-1, 2), then what are the coordinates of point B?

A. (-1, 8)
B. (9, 2)
C. (5, 2)
D. (11, 2)
E. (11, 8)

sindhuagarwal · Answer

The line x = 5 is a vertical line passing through the point (5, 0) on the x-axis. Since it is given that this line is the perpendicular bisector of the line segment AB, point B must be symmetrically located on the other side of x = 5, equidistant from point A.

The distance between points A and B is the horizontal distance from A to the line x = 5, which is twice the distance from A to x = 5. Therefore, the x-coordinate of point B is 5 + 2 * (distance from A to x = 5).

The distance from A to x = 5 is 5 - (-1) = 6.

So, the x-coordinate of point B is 5 + 2 * 6 = 17.

Now, the y-coordinate of point B remains the same as that of point A, which is 2.

Therefore, the coordinates of point B are (17, 2).

The correct answer is not among the given options. Please double-check the options or the question. If there's a mistake in the options, the closest one is (D) (11, 2).

DrAnkita91 · Answer

option B C D... how to choose between these 3? please help

Bunuel · Answer

In an XY coordinate plane, the line x = 5 is a perpendicular bisector of the line segment AB. If the coordinates of point A are (-1, 2), then what are the coordinates of point B?

A. (-1, 8)
B. (9, 2)
C. (5, 2)
D. (11, 2)
E. (11, 8)

The line x = 5 represents a vertical line located at x = 5. Given that it serves as the  perpendicular bisector  of segment AB, AB must be a horizontal line segment, implying that all points on AB share the same y-coordinate. Thus, since the coordinates of A are (-1, 2), the coordinate of B must be (x, 2). Furthermore, since the line x = 5 divides AB equally, the distance of A from x = 5 must be equal to the distance of B from the line. A is 5 - (-1) = 6 units away from x = 5, therefore B is also 6 units to the right and positioned at 5 + 6 = 11. Consequently, the coordinates of B are (11, 2).

Answer: D.

In an XY coordinate plane, the line x = 5 is a perpendicular bisector

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In an XY coordinate plane, the line x = 5 is a perpendicular bisector

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